Results 231 to 240 of about 1,289,599 (266)

Equality of two-variable functional means generated by different measures

Aequationes mathematicae, 2011
Two-variable functional means, \(M_{f,g;\mu}\) defined by \[ M_{f,g;\mu}(x,y)= \Biggl({f\over g}\Biggr)^{-1}\left({\int_{[0,1]} f(tx+ (1- t)y)\,d\mu(t)\over \int_{[0,1]} g(tx+ (1- t)y)\,d\mu(t)}\right) \] for real-valued continuous functions \(f\) and \(g\) defined on a real open interval \(I\), \(\mu\) a measure on the Borel sets of \([0,1]\), \(g\) a
Losonczi, László, Páles, Zsolt
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A general Minkowski-type inequality for two variable Gini means

Publicationes Mathematicae Debrecen, 2000
The authors offer as ``main result'' necessary and sufficient conditions on \((a_0,b_0,a_1,b_1,a_2,b_2)\in\mathbb R^6\) for \(S_{a_0,b_0}(x+y)\leq S_{a_1,b_1}(x)+S_{a_2,b_2}(y)\) for all \((x,y)\in ]0,\infty[^4\) and the consequence that the inequality is `best' if \((a_0,b_0)=(a_1,b_1)=(a_2,b_2).\) Here \(S_{a,b}((u,v))\) is defined by \((\frac{u^a +v^
Czinder, P., Páles, Zs.
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Approximation of differentiable functions of two variables in the mean by fourier sums

Ukrainian Mathematical Journal, 1983
This equation gives the solution of the Kolmogorov--Nikol'skii problem if c1~m/n~ci, where ci and c2 are positive constants, since the first term on the right-hand side is the principal term in this case only. We prove the following theorem. TI{EOREH i.
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Characterization of groups of involutions by means of composite functional equations in two variables

Acta Mathematica Hungarica, 2021
In this short note the following result is proved. Given an arbitrary group \((G,\cdot)\) the following conditions are pairwise equivalent: (1) \(G\) is involutive; (2) The functional equation \( f(xf(y)) = f(f(x))y^{-1} \text{ for all } x,y\in G \) admits a solution \(f:G\to G\); (3) The functional equation \( f(xf(y)) = y^{-1}f(f(x)) \text{ for all }
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Equality of two variable weighted means: reduction to differential equations

aequationes mathematicae, 1999
In this remarkable paper, the author considers the functional equation in a real interval \[ \Phi^{-1} \left( {\Phi (x) F(x) + \Phi (y) F(y)} \over {F(x)+ F(y) } \right) = \Psi^{-1} \left( {\Psi (x) G (x)+ \Psi (y) G(y)} \over {G(x)+G(y) } \right) \tag{*} \] of the equality of two quasiarithmetic means weighted by some weightfuctions \(F\) and \(G ...
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Approximation by Nörlund means of double fourier series to continuous functions in two variables

Constructive Approximation, 1987
Let f(x,y) be continuous and \(2\pi\)-periodic in each variable. In this paper the rate of uniform approximation, by Nörlund means, of the rectangular partial sums of double Fourier series of f(x,y) is studied. The first two theorems relate to the double Fourier series. As a special case the authors obtain the rate of uniform approximation to functions
Móricz, F., Rhoades, B. E.
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The approximation of a H�lder class of two variables by Riesz spherical means

Mathematical Notes of the Academy of Sciences of the USSR, 1974
For periodic functions of the Holder class H2α (0 < α≤1) defined in the two-dimensional space D2, we find the asymptotic form as R → + ∞ of the quantity $$\mathop {\sup }\limits_{f \in H_2^\alpha } \parallel S_R^\delta (x,f) - f(x)\parallel _{C(E_2 )} \left( {\delta > \frac{1}{2} + \alpha } \right),$$ where SRδ is the Riesz spherical mean of ...
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Comparison of two variable homogeneous means

1992
In this paper we give necessary and sufficient conditions for the inequality $$\left( * \right)M\left( {x,y} \right) \leq N\left( {x,y} \right),\quad x,y \in \left[ {\alpha ,\beta } \right],$$ (*) where 0 < α < β < ∞ are fixed values and M: ℝ+ × ℝ+ → ℝ+ and N: ℝ+ × ℝ+ → ℝ+ belong to one of the following classes of means: $${D_{a,b}}\left(
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An Effective and Adaptable K-means Algorithm for Big Data Cluster Analysis

Pattern Recognition, 2023
Haize Hu, Jianxun Liu
exaly  

K-means clustering algorithms: A comprehensive review, variants analysis, and advances in the era of big data

Information Sciences, 2023
Absalom E Ezugwu, Laith Abualigah, Belal Abuhaija   +2 more
exaly